Common Knowledge of a Multivariate Aggregate Statistic.

If a stochastically monotone function of asymmetrically informed individuals' expectations of a random vector is common knowledge up to some observation error, then all the individuals must agree on their expectations. This result generalizes the 1986 theorem of R. D. McKelvey and T. Page from random variables to random vectors. It holds for general information structures given by sigma-algebras. Copyright 1995 by Economics Department of the University of Pennsylvania and the Osaka University Institute of Social and Economic Research Association.